Factors & Multiples
GCF, LCM, and prime factorization
Start with the basics and progress through 6 lessons. Each lesson builds on the previous one.
0 of 6 lessons done
In This Topic (6 lessons)
Factors and Multiples
Learn what factors and multiples are, how to find them, and why they're important in math.
Prime Factorization
Learn how to break down any number into its prime factor building blocks.
Prime and Composite Numbers
Learn to identify prime numbers (divisible only by 1 and themselves) and composite numbers (having more than two factors).
Greatest Common Factor (GCF)
Learn how to find the greatest common factor of two or more numbers using multiple methods.
Least Common Multiple (LCM)
Learn how to find the smallest number that is a multiple of two or more numbers.
Euclidean Algorithm
Find the greatest common factor of any two numbers by repeated division with remainder, and use it to simplify fractions and find the LCM.
Factors are numbers that divide evenly into another number; multiples are products of a number with integers. Understanding factors and multiples is essential for simplifying fractions, finding common denominators, and solving problems in algebra and number theory.
What You'll Learn
- Find all factors of a number
- List multiples of a number
- Distinguish between factors and multiples
- Find GCF and LCM
- Apply to fraction operations
Frequently Asked Questions
What is the difference between factors and multiples?
Factors divide INTO a number (factors of 12: 1,2,3,4,6,12). Multiples are what you get when you multiply BY a number (multiples of 3: 3,6,9,12...).
How do I find all factors?
Test division by 1, 2, 3, etc. until you reach the square root. Each factor has a pair.
What is the relationship between GCF and LCM?
For any two numbers a and b: GCF(a,b) × LCM(a,b) = a × b.